Currently used algorithms for providing a laser shot file using finite laser pulse sizes, such as 1 mm or 2 mm, deliver a laser shot file which is an approximation to the intended theoretical ablation profile. This is mainly based on the fact that the used algorithms only use the theoretically total removed volume per pulse, irrespective whether a standard or a customized treatment is planned.
The theoretical ablation profile relates to the desired refractive correction compensating a determined vision error of an eye. The desired refractive correction may be based on diagnostic data obtained by at least one of a subjective refractive error and a measured objective refractive error. The measured refractive error may be obtained by at least one of a wavefront sensor, topographical measurement device or a pachymetry measurement device. Low order aberrations may be determined by a subjective refractive error, e.g. considering the verbal feedback of a patient.
Classical ablation algorithms further induce biodynamic effects which are in general expressed by unintended induced shape aberrations. To compensate for these unintended induced shape aberrations additional ablation of corneal tissue may be necessary, which may cause incremental modifications to the desired ablation profile. Also the fact that the size of pulses, which comprises the pulse diameter, is not infinitely small may cause the need to create a transition zone around the actually relevant central ablation zone.
The final shape of a wavefront may be created by a superposition of known two dimensional surfaces of a known shape. For each of these known shapes a scaling factor may be obtained, e.g. by a software, to get the best representation of the wavefront deformation.
There are various sets of functions which create the already mentioned known two dimensional surfaces. Here in the following the Zernike Polynomial system will be briefly described.
The amplitudes A of Zernike polynomials can be represented mathematically as follows.An,mπ
Where n represents the Zernike mode, i.e. the main order of the polynomial, which is the primary parameter in the classification of the radial behavior of the polynomial. The parameter n gives more or less the radial distribution. The larger the order n is, the outer in the periphery the major characteristics are located.
The angular characteristic of the polynomial is specified by the parameter m, which describes how often a certain structure is repeated in azimutal direction, i.e. the parameter m gives the azimutal symmetry of the polynomial. The larger the value for m, the more sophisticated the azimutal profile of the polynomial, i.e. the more structures along one azimutal circle can be detected. The parameter π describes the symmetry characteristic of the polynomial, i.e., even or odd.
Reference is made to FIG. 15 which illustrates the behavior of a graphical representation of Zernike polynomials with corresponding parameters. The OSA standard notation (Thibos et al., 2000) as used in FIGS. 14 and 15 for the Zernike polynomials Z is defined as follows:Znπ·m 
The original wavefront error W of the eye can be reconstructed by a linear combination of the calculated Zernike polynomials Z, taking into account their individual amplitudes An,mπ using the following equation:
      W    ⁡          (              ρ        ,        φ            )        =            ∑              n        ,        m        ,        π              ⁢                  A                  n          ,          m                π            ⁢                        Z                      n            ,            m                    π                ⁡                  (                      ρ            ,            φ                    )                    
The notation Zn,mπ corresponds to Znπ·m of the OSA standard notation. The parameters ρ, φ represent the coordinate values. In the following, the Bausch & Lomb notation (B&L notation) is used.
U.S. Pat. No. 6,090,100 relates to an excimer laser system for correction of vision with reduced thermal effects. It specifically relates to an apparatus and method for controlling the excimer laser system for removing tissue from the eye to perform various types of corrections, such as myopia, hyperopia, and astigmatism correction. In one disclosed embodiment, the excimer laser system provides a relatively large pulse size which provides a relatively large coverage of treatment area per shot. While using such large pulse sizes, the shots are generally not “adjacent” to each other but the pulses overlap to generate the desired degree of ablation at a particular point. For calculating the result of the overlapping pulses, an algorithm is used. In one method of calculating treatment patterns using large, fixed pulse sizes distributed throughout the treatment area, a dithering algorithm is used. Specific reference is made to a rectangular dithering, circular dithering and a line-by-line oriented dithering. Using any variety of shot dithering methods, an array of shots is created for a fixed pulse size spread over a treatment area to correct to the desired degree of ablation. For the respective array, a grid is used with a constant grid width between individual grid positions. With the known dither methods, the shape of the desired ablation profile, which usually is a continuous profile, has to be transferred into a whole-numbered discrete density distribution. Here, the continuous profile represents a planned ablation and the whole-numbered discrete density distribution represents a series of ablating flying spot laser pulses. The residual structure, i.e., the difference between the planned and the achieved profile, has to be minimised. Exact solutions can principally be found numerically but not in a reasonable time. Therefore, for this purpose, dither algorithms are used. The profile is discretised on a given grid. Using a cost function or merit function the algorithm decides for each position of the grid whether to place a shot or not. For this decision, usually only a few neighbouring positions of the grid are taken into account. This dither algorithm saves calculation time without the need that the real size of the pulse is taken into account. It is sufficient to know the volume which is ablated with one laser shot. However, under certain conditions, the known dither algorithms produce artefacts in parts of the profile, e.g., in low-density regions where the next neighbouring shot is too far away. Artefacts may also be produced in high-density regions where at nearly every position, a shot is placed. The positions with no shot also have too large a distance for the assumption that only a few neighbour positions are necessary.